How many numbers between $1$ and $100$ (inclusive) are divisible by $3$ or $10$ ?
Answer: There are $33$ numbers divisible by $3$ between $1$ and $100$, and $10$ numbers divisible by $10$ between $1$ and $100$. So, you might think there are $33 + 10 = 43$ numbers divisible by one or the other, but this is overcounting something. We're counting every number which is divisible by both $3$ and $10$ twice. So, for example, $30$ is counted once as a number divisible by $3$, and then again as a number divisible by $10$. So, we need to count how many numbers are divisible by both $3$ and $10$ and subtract this from what we had before. Being divisible by both $3$ and $10$ is the same thing as being divisible by $30$, so there are $3$ numbers between $1$ and $100$ divisible by both. Subtracting, there are $43 - 3 = 40$ numbers divisible by $3$ or $10$.